International Journal of Modern Physics B

In this review paper, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of the available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range correlated random-site disorder, and (iii) random anisotropy.

Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of this review is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.

A method is proposed for the quantum-mechanical determination of the eigenstates and eigenvalues of a particle (e.g. an electron) in a potential of general shape. For such systems the method allows one to calculate the exact solutions of the stationary Schrödinger equation. For the application of this method any well-known reference system is needed. A transition from the stationary reference system to the stationary system under investigation is performed by means of the time-dependent Schrödinger equation. The results are compared with various standard methods; alternative numerical methods will be discussed critically.

Studying the quantum size effects on the exciton energy of two-dimensional CdS quantum dots in the single band effective mass approximation for both electron and hole, we use a finite confinement in the x–y plane and we assume also that the induced charge is spread along a very thin interface in the z-direction. Solving the Schrödinger equation with a new numerical method, which is called potential morphing method, we obtain the corresponding energy within the self-consistent Hartree scheme. Excellent agreement is obtained with the experimental values of exciton energies for various sizes of CdS quantum dots in the strong, medium and weak confinement limit.

By means of Tao, Sheng and Lin's generized molecular field theory, the temperature dependence of the order parameter dQ/dT|_Tc has been calculated. All the parameters in the calculation are fixed by experiments like the previous paper. There is no adjustable parameter. Our calculated value of dQ/dT|_Tc ~ 1%K^-1 agree well with experiments. The new puzzle of small value of dQ/dT|_Tc does not existence.

The charge density wave (CDW) in the layered compound 2H-TaSe₂ at low temperatures has a commensurate phase, which causes super lattice points to appear in the Brillöuin zone of the undistorted phase. A Born-von Karman formalism has been employed for the calculation of phonon frequency distribution curves of 2H-TaSe₂ both in the normal and in the commensurate charge density wave (CCDW) phases. A folding technique has been adopted for the calculation in the CCDW phase. The phonon distribution for both the phases have been reported. With these distributions the thermal properties such as specific heat capacity, Debye Waller factor W(k) and thermal conductivity have been worked out, and compared with the available experimental results.

We first introduce the basic ingredients of the eigenfunctional theory, and show that a D-dimensional quantum many-particle system is mapped into a (D+1)-dimensional time-depending single-particle problem, and in the representation of the eigenfunctionals of the particle propagator, the particles become free. Then using this method, we study five kinds of quantum many-particle systems: interacting boson system, repulsive, attractive interacting fermion systems, Hubbard model and single-impurity scattering in one-dimensional fermion system, and demonstrate that the microscopic Bogoliubov theory and the phenomenological Bijl–Feynman theory of the bosons are closely related, and apart from an anti-symmetry factor Det‖e^ik_j·x_l‖ the ground state wave function of the repulsive interacting fermion system has a similar form to that of the interacting boson system. Moreover, we show that the attractive interacting fermion system has a sound-type excitation spectrum like that in the interacting boson system. For one-dimensional Hubbard model we calculate the electron Green's function, and charge and spin density–density correlation functions which are consistent with the exact ones obtained by the Bethe ansatz and numerical calculations, and show that the ground state energy is increasing with U, and the electrons has single-occupied constraint in the large U limit. Finally, we demonstrate clearly the evolution of the system from its ultraviolet fixed point to infrared critical fixed point as the impurity potential increases. At the infrared critical fixed point, the fermion Green's function shows that the fermions are completely reflected on the impurity site.

A driven diffusive system (DDS) is a lattice-gas in contact with a thermal bath in the presence of an external field. Such DDS constantly gains (losses) energy from (to) the driving field (thermal bath) and therefore, for long enough time, it reaches a non-equilibrium steady-state (NESS) with a generally unknown statistical distribution. It is found that if the constant driving is replaced by an oscillatory field of magnitude E and period τ, the system exhibits a crossover from NESS to a quasi-equilibrium state (QES) driven by τ. The crossover behavior is characterized by a typical crossover time which is proportional to the lattice side and consequently relevant to confined systems.

The frequency (100Hz–1MHz) and temperature (30–575°C) dependence of electrical properties of calcium doped (Ca = 0.01, 0.05, 0.1) sodium bismuth titanate (NBT) was investigated by impedance spectroscopy. The data is used to analyze the effect of calcium concentration on the electrical properties of NBT. The frequency explicit plots of Z′′ versus frequency at various temperatures shows peaks in the higher temperature range (>400°C). The relaxation peaks are affected by the doping. The AC conductivity values are computed from the impedance data. DC conductivity has been measured in the temperature range of 30–400°C. The activation energies have been evaluated from the data. From the studies of dielectric constant as a function of temperature, it is observed that diffuse phase transition (DPT) is exhibited in these samples.